When searching online (e.g. on eBay), add to your search 22AWG
That will bring you to results where the data wires are made with 26-28 AWG (rather thin) but the power wires are in 22 AWG.
A 22 AWG wire has a resistance of about 0.055 ohm/meter so at 1 A a 1 m cable will cause only about 0.1 V drop.
(for comparison, a 28 AWG wire as those used for USB data has a resistance 4 times higher)